{
 "cells": [
  {
   "cell_type": "raw",
   "metadata": {},
   "source": [
    "Text provided under a Creative Commons Attribution license, CC-BY.  All code is made available under the FSF-approved BSD-3 license.  (c) Lorena A. Barba, Gilbert F. Forsyth 2017. Thanks to NSF for support via CAREER award #1149784."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[@LorenaABarba](https://twitter.com/LorenaABarba)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12 steps to Navier–Stokes\n",
    "=====\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the previous step, we solved the [2D Burgers' equation](./10_Step_8.ipynb): an important equation in the study of fluid mechanics because it contains the full convective nonlinearity of the flow equations. With that exercise, we also build the experience to incrementatlly code a Navier–Stokes solver.\n",
    "\n",
    "In the next two steps, we will solve Laplace and then Poisson equation. We will then put it all together!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Step 9: 2D Laplace Equation\n",
    "----\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is Laplace's equation in 2D:\n",
    "\n",
    "$$\\frac{\\partial ^2 p}{\\partial x^2} + \\frac{\\partial ^2 p}{\\partial y^2} = 0$$\n",
    "\n",
    "We know how to discretize a 2nd order derivative. But think about this for a minute — Laplace's equation has the features typical of diffusion phenomena. For this reason, it has to be discretized with *central differences*, so that the discretization is consistent with the physics we want to simulate. \n",
    "\n",
    "The discretized equation is:\n",
    "\n",
    "$$\\frac{p_{i+1, j}^n - 2p_{i,j}^n + p_{i-1,j}^n}{\\Delta x^2} + \\frac{p_{i,j+1}^n - 2p_{i,j}^n + p_{i, j-1}^n}{\\Delta y^2} = 0$$\n",
    "\n",
    "Notice that the Laplace Equation does not have a time dependence — there is no $p^{n+1}$.  Instead of tracking a wave through time (like in the previous steps), the Laplace equation calculates the equilibrium state of a system under the supplied boundary conditions.  \n",
    "\n",
    "If you have taken coursework in Heat Transfer, you will recognize the Laplace Equation as the steady-state heat equation.  \n",
    "\n",
    "Instead of calculating where the system will be at some time $t$, we will iteratively solve for $p_{i,j}^n$ until it meets a condition that we specify.  The system will reach equilibrium only as the number of iterations tends to $\\infty$, but we can approximate the equilibrium state by iterating until the change between one iteration and the next is *very* small.  \n",
    "\n",
    "Let's rearrange the discretized equation, solving for $p_{i,j}^n$:\n",
    "\n",
    "$$p_{i,j}^n = \\frac{\\Delta y^2(p_{i+1,j}^n+p_{i-1,j}^n)+\\Delta x^2(p_{i,j+1}^n + p_{i,j-1}^n)}{2(\\Delta x^2 + \\Delta y^2)}$$\n",
    "\n",
    "Using second-order central-difference schemes in both directions is the most widely applied method for the Laplace operator. It is also known as the **five-point difference operator**, alluding to its stencil."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to solve Laplace's equation numerically by assuming an initial state of $p=0$ everywhere. Then we add boundary conditions as follows:\n",
    "\n",
    "$p=0$ at $x=0$\n",
    "\n",
    "$p=y$ at $x=2$\n",
    "\n",
    "$\\frac{\\partial p}{\\partial y}=0$ at $y=0, \\ 1$\n",
    "\n",
    "Under these conditions, there is an analytical solution for Laplace's equation:\n",
    "\n",
    "$$p(x,y)=\\frac{x}{4}-4\\sum_{n=1,odd}^{\\infty}\\frac{1}{(n\\pi)^2\\sinh2n\\pi}\\sinh n\\pi x\\cos n\\pi y$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Exercise"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Write your own code to solve Poisson's equation using loops, in the style of coding used in our first lessons. Then, consider the demonstration of how to write it using functions (below) and modify your code in that style. Can you think of reasons to abandon the old style and adopt modular coding?\n",
    "\n",
    "Other tips:\n",
    "\n",
    "+ Visualize each step of the iterative process\n",
    "+ Think about what the boundary conditions are doing\n",
    "+ Think about what the PDE is doing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using functions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember the lesson on writing [functions with Python](./11_Defining_Function_in_Python.ipynb)? We will use that style of code in this exercise.\n",
    "\n",
    "We're going to define two functions: one that plots our data in a 3D projection plot and the other that iterates to solve for $p$ until the change in the [L1 Norm][1] of $p$ is less than a specified value.   \n",
    "\n",
    "[1]: http://en.wikipedia.org/wiki/Norm_(mathematics)#Taxicab_norm_or_Manhattan_norm "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "from matplotlib import pyplot, cm\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot2D(x, y, p):\n",
    "    fig = pyplot.figure(figsize=(11, 7), dpi=100)\n",
    "    ax = fig.gca(projection='3d')\n",
    "    X, Y = numpy.meshgrid(x, y)\n",
    "    surf = ax.plot_surface(X, Y, p[:], rstride=1, cstride=1, cmap=cm.viridis,\n",
    "            linewidth=0, antialiased=False)\n",
    "    ax.set_xlim(0, 2)\n",
    "    ax.set_ylim(0, 1)\n",
    "    ax.view_init(30, 225)\n",
    "    ax.set_xlabel('$x$')\n",
    "    ax.set_ylabel('$y$')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `plot2D` takes three arguments, an x-vector, a y-vector and our p matrix.  Given these three values, it produces a 3D projection plot, sets the plot limits and gives us a nice viewing angle.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$p_{i,j}^n = \\frac{\\Delta y^2(p_{i+1,j}^n+p_{i-1,j}^n)+\\Delta x^2(p_{i,j+1}^n + p_{i,j-1}^n)}{2(\\Delta x^2 + \\Delta y^2)}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def laplace2d(p, y, dx, dy, l1norm_target):\n",
    "    l1norm = 1\n",
    "    pn = numpy.empty_like(p)\n",
    "\n",
    "    while l1norm > l1norm_target:\n",
    "        pn = p.copy()\n",
    "        p[1:-1, 1:-1] = ((dy**2 * (pn[1:-1, 2:] + pn[1:-1, 0:-2]) +\n",
    "                         dx**2 * (pn[2:, 1:-1] + pn[0:-2, 1:-1])) /\n",
    "                        (2 * (dx**2 + dy**2)))\n",
    "            \n",
    "        p[:, 0] = 0  # p = 0 @ x = 0\n",
    "        p[:, -1] = y  # p = y @ x = 2\n",
    "        p[0, :] = p[1, :]  # dp/dy = 0 @ y = 0\n",
    "        p[-1, :] = p[-2, :]  # dp/dy = 0 @ y = 1\n",
    "        l1norm = (numpy.sum(numpy.abs(p[:]) - numpy.abs(pn[:])) /\n",
    "                numpy.sum(numpy.abs(pn[:])))\n",
    "     \n",
    "    return p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`laplace2d` takes five arguments, the `p` matrix, the `y`-vector, `dx`, `dy` and the value `l1norm_target`.  This last value defines how close the `p` matrix should be in two consecutive iterations before the loop breaks and returns the calculated `p` value.  \n",
    "\n",
    "Note that when executing the cells above in your own notebook, there will be no output.  You have *defined* the function but you have not yet *called* the function.  It is now available for you to use, the same as `numpy.linspace` or any other function in our namespace.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "##variable declarations\n",
    "nx = 31\n",
    "ny = 31\n",
    "c = 1\n",
    "dx = 2 / (nx - 1)\n",
    "dy = 2 / (ny - 1)\n",
    "\n",
    "\n",
    "##initial conditions\n",
    "p = numpy.zeros((ny, nx))  # create a XxY vector of 0's\n",
    "\n",
    "\n",
    "##plotting aids\n",
    "x = numpy.linspace(0, 2, nx)\n",
    "y = numpy.linspace(0, 1, ny)\n",
    "\n",
    "##boundary conditions\n",
    "p[:, 0] = 0  # p = 0 @ x = 0\n",
    "p[:, -1] = y  # p = y @ x = 2\n",
    "p[0, :] = p[1, :]  # dp/dy = 0 @ y = 0\n",
    "p[-1, :] = p[-2, :]  # dp/dy = 0 @ y = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's try using our `plot2D` function to look at our initial conditions.  If the function has been correctly defined, you should be able to begin typing `plot2D` and hit the **tab** key for auto-complete options.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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KpfDBBx8YbtNf4PWT2f1ShauG86yMuKCBqDGV3kckSUI8Hteqd6JyU76wIhqN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\nsHES6IQQQgghbNz/BdnM+87PASW+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efdac44fb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot2D(x, y, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It worked!  This is the initial state of our problem, where the value of `p` is zero everywhere except for along $x=2$ where $p=y$.  Now let's try to run our `laplace2d` function with a specified L1 target of .01\n",
    "\n",
    "[Hint: if you are having trouble remembering the order in which variables are sent to a function, you can just type `laplace2d(` and the iPython Notebook will put up a little popup box to remind you]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = laplace2d(p, y, dx, dy, 1e-4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try plotting this new value of `p` with our plot function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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96FaB67q48cYb8dd//dexx0ejEZrNJhqNyvhwYQRBgNFohH7frHdWXtJmZ1hU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\nEzoAgLkATO21N3iMpXwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7efda9996908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot2D(x, y, p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn More"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The [next step](./13_Step_10.ipynb) will be to solve Poisson's equation. Watch **Video Lesson 11** on You Tube to understand why we need Poisson's equation in CFD."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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bEqvqyDqzzi4QnqAwB/uZbvzK6LDWwPPQKgd2J30H4imq1ebZQ+85lRLAzL01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\nREQERED/2Q==\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/ZjfxA3qq2Lg\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7efda996b438>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('ZjfxA3qq2Lg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And for a detailed walk-through of the discretization of Laplace and Poisson equations (steps 9 and 10), watch **Video Lesson 12** on You Tube:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/iwL8ashXhWU\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x7efda82001d0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('iwL8ashXhWU')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<link href='http://fonts.googleapis.com/css?family=Fenix' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Alegreya+Sans:100,300,400,500,700,800,900,100italic,300italic,400italic,500italic,700italic,800italic,900italic' rel='stylesheet' type='text/css'>\n",
       "<link href='http://fonts.googleapis.com/css?family=Source+Code+Pro:300,400' rel='stylesheet' type='text/css'>\n",
       "<style>\n",
       "    @font-face {\n",
       "        font-family: \"Computer Modern\";\n",
       "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
       "    }\n",
       "    div.cell{\n",
       "        width:800px;\n",
       "        margin-left:16% !important;\n",
       "        margin-right:auto;\n",
       "    }\n",
       "    h1 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\n",
       "    h2 {\n",
       "        font-family: 'Fenix', serif;\n",
       "    }\n",
       "    h3{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "        margin-top:12px;\n",
       "        margin-bottom: 3px;\n",
       "       }\n",
       "\th4{\n",
       "\t\tfont-family: 'Fenix', serif;\n",
       "       }\n",
       "    h5 {\n",
       "        font-family: 'Alegreya Sans', sans-serif;\n",
       "    }\t   \n",
       "    div.text_cell_render{\n",
       "        font-family: 'Alegreya Sans',Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
       "        line-height: 135%;\n",
       "        font-size: 120%;\n",
       "        width:600px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "    }\n",
       "    .CodeMirror{\n",
       "            font-family: \"Source Code Pro\";\n",
       "\t\t\tfont-size: 90%;\n",
       "    }\n",
       "/*    .prompt{\n",
       "        display: None;\n",
       "    }*/\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 50pt;\n",
       "\t\tline-height: 100%;\n",
       "        color:#CD2305;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\t\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 300;\n",
       "        font-size: 16pt;\n",
       "        color: #CD2305;\n",
       "        font-style: italic;\n",
       "        margin-bottom: .5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "    }\n",
       "    \n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "        }  \n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.core.display import HTML\n",
    "def css_styling():\n",
    "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
    "    return HTML(styles)\n",
    "css_styling()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> (The cell above executes the style for this notebook.)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
